Scheduling trucks in fruit cross docks as an open shop problem with edge colouring

Cross docking is believed to be an efficient approach to control the physical flow of the supply chain. Due to its importance, companies these days feel the necessity of careful planning of the inbound and outbound flows. As a result, they can reach customer satisfaction milestone and also time and cost reduction. In this paper, we study fruit and vegetable cross docks which are different than the other forms of cross docks. In such cross docks, time plays an important role and it must be reduced to the minimum length possible so that we can decrease the cooling and spoilage expenses to a great extent. We modelled the inbound docks as an open shop problem in order to minimise the unloading time of the inbound trucks, then we developed a heuristic solution procedure method based on graph theory to deal with this problem.